Weak-star continuous homomorphisms and a decomposition of orthogonal measures (Q797806)

We consider the set \(S(\mu)\) of complex-valued homomorphisms of a uniform algebra A which are weak-star continuous with respect to a fixed measure \(\mu\). The \(\mu\)-parts of \(S(\mu)\) are defined, and a decomposition theorem for measures in \(A^{\perp}\cap L^ 1(\mu)\) is obtained, in which constituent summands are mutually absolutely continuous with respect to representing measures. The set \(S(\mu)\) is studied for T-invariant algebras on compact subsets of the complex plane and also for the infinite polydisc algebra.